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Web Hosting and Cloud Computing Control Panels
Well, probably yes if you have sites pointing to that IP, you will need to update the DNS records for them to work again.
Google Cloud uses NAT, so they route the traffic from your public IP to your internal IP and the Internal IP's are set up with DHCP so they will change very offend. This means that you need to correctly set the software to be aware of that network configuration, otherwise when you create accounts they will use the internal IP. Your server will work fine if your public IP changes and you have everything configured with internal IP's, otherwise, you need to update the configs with the correct public IP if you had it set up in your server. Changing the public IP is not something you should really do and Google would not change your IP either. I assume you don't have a fixed IP, in that case, you need one. It cost extra. But you should pay it to make sure it does not change. You don't want the IP of your server changing if you plan to run public services from it.
If you have sites pointing to that IP and it changes, they will be offline.
If you are running a DNS service from your server, things get a bit more tricky with NAT. Usually, you don't want NAT for a public server either. In a datacenter often people don't use NAT at all but now its familiar with cloud providers because IPv4 is depleted. Google Cloud has NAT and firewall by default, its actually very nice, but you need to setup your networking first, firewall and routes.
That setup is far more complicated than just using a simple provider with a public direct IP (like most of them). Not that its worse, it's probably even better if you run clusters and have more experience. My point is that Google Cloud is likely to be way over your head here based on the questions you ask. The networking provisioning is more complex. Also, Google Cloud does not allow emails out from their services, and neither they allow Reverse DNS's to your IP's (which you need for email server).
If you plan to do any emailing with your Virtualmin servers, you will be for a shocking surprise that it will not work properly from your Google Instance and you will need to use an external email service.
Before doing anything, first research why your public IP was changed in the first place. I also have some Google Cloud Instances and the IP's never ever change.